Recent questions tagged mock-test-series-2015

Find the area enclosed by the curve $y=1x$ and $y= -|x-1|+1$

asked Jan 21, 2015 by meena.p

1 answer

find the area bounded by the lines $y= 4x+5,y=5-x$ and $4y= x+5$

asked Jan 21, 2015 by meena.p

1 answer

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi/2} \large\frac{\cos x}{1+ \cos x+ \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi} \large\frac{x}{1- \cos \alpha \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

The cost of $4kg$ Onion,$3kg$ wheat and $2kg$ rice is $\$60$. The cost of $2\;kg$ onion,$4\;kg$ wheat and $6\;kg$ rice is $\$90$. The cost of $6\;kg$ onion, $2\;kg$ wheat and $3\;kg$ rice is $\$70$. Find the cost of each item per kg by matrix method.

asked Jan 21, 2015 by meena.p

1 answer

If $x \sqrt {1+y} +y\sqrt {1+x}=0$. Then prove that $(1+x)^2 \large\frac{dy}{dx}$$+1=0$

asked Jan 21, 2015 by meena.p

0 answers

A coin is biased , so that head is 3 times as to occur as tail. If the coin is tossed twice. Find the probability distribution of number of tails.

asked Jan 21, 2015 by meena.p

1 answer

In a die game , a player pays a stake of $\$1$ for each throw of a die. She receives $\$5$, if the die shows a 3, $\$2$ if the die shows 1 or 6 and nothing otherwise. What is the player expected profit per throw over a long series of throws?

asked Jan 21, 2015 by meena.p

1 answer

The volume of a cube is increasing at a rate of $9\;cm^2/s$ . How fast is the surface area increasing . When the length of the edge is $10\;cm$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\tan \bigg[\sin^{-1}\bigg(\large\frac{2x}{1+x^2}\bigg)+$$\cos^{-1} \bigg( \large\frac{1-y^2}{1+y^2}\bigg)\bigg]$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\sin (2 \tan ^{-1} \large\frac{1}{3})$$+ \cos(\tan^{-1} 2 \sqrt 2)$

asked Jan 21, 2015 by meena.p

0 answers

Find the inverse of $A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$ by elementary transformation and hence solve the following system of linear equation : $2x+y=3; 4x+2y=6$

asked Jan 21, 2015 by meena.p

1 answer

If $f(x) = \left\{ \begin{array} {1 1} 1 & \quad, \text{ if $ x \leq$ 3 }\\ ax+b & \quad, \text{if $3 < x < 5$ } \\ 7 & \quad, \text{ if $ 5 \leq x $ } \end{array} \right.$ Determine the values if a and b so that $f(x)$ is continuous?

asked Jan 21, 2015 by meena.p

1 answer

If $ f(x) = \left\{ \begin{array} {1 1} \large\frac{ 2^{x+2}-16}{4^x-16}, & \quad\text{ if $x \neq 2$ } \end{array} \right. $ is a continuous at $x=2,$ then find k ?

asked Jan 21, 2015 by meena.p

1 answer

$\begin{align} \int \limits_{\large\frac{\pi}{3}}^{\large\frac{\pi}{2}}\frac{\sqrt {1+\cos x}}{(1- \cos x)^{5/2}}dx \end{align}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $ \int \large\frac{dx}{(x-1)\sqrt {2x+3}}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate = $\int \large\frac{x^2}{(x \sin x +\cos x)^2}$

asked Jan 21, 2015 by meena.p

1 answer

Solve the differential equation : $(x+2y^2) \large\frac{dy}{dx}$$=y$, given that when $x=2$ and $y=1$. If x devotes the percentage of who are intelligent and y denotes the percentage of people who are work holic, find x when $y=2 \%$ workoholics are always preferable. Do you agree ?

asked Jan 21, 2015 by meena.p

1 answer

Find the equation of the plane containing the line intersection of the plane $x+y+z-6=0$ and $2x+3y+4z+5=0$ and Passing through the pay $(1,1,1)$

asked Jan 21, 2015 by meena.p

1 answer

Find the shortest distance between the lines whose vector equations are : $\overrightarrow{r}= (\hat i+2 \hat j+3 \hat k)+ \lambda (2 \hat i+ 3 \hat j +4 \hat k)$ and $\overrightarrow{r}= (2 \hat i+4 \hat j+5 \hat k)+ (4 \hat i+ 6 \hat j +8 \hat k)$

asked Jan 21, 2015 by meena.p

1 answer

Using the properties of determines evaluate : $\begin{vmatrix} 1 & a & a^2-bc \\1 & b & b^2-ca \\1 & c & c^2-ab\end{vmatrix}$

asked Jan 21, 2015 by meena.p

1 answer

Let $f : N \to R$ be a function defined as $f(x)=4x^2+12x+15$. Show that $f: N \to R$ is invertible. Find the inverse of f

asked Jan 21, 2015 by meena.p

0 answers

Differentiate $\sqrt {\tan \sqrt {x}}$ with respect to x

asked Jan 21, 2015 by meena.p

1 answer

The side of a square is increasing at rate of $0.2\;cm/s$ Find the rate of increase of x perimeter of the square.

asked Jan 21, 2015 by meena.p

1 answer

Find the order and degree of the following differential equation : $\bigg( \large\frac{d^2y}{dx^2}\bigg)^3+\bigg(\large\frac{dy}{dx}\bigg)^2$$+\sin \bigg( \large\frac{dy}{dx}\bigg)$$+1=0$

asked Jan 21, 2015 by meena.p

1 answer

Find the area of the parallelogram whose adjacent sides are $\overrightarrow{a}= \hat i+ 2 \hat j +3 \hat k$ and $\overrightarrow{b}= 3 \hat i - 2 \hat j + \hat k$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $\begin{vmatrix}x+2 & x+3 & x+2a\\x+3 & x+4 & x+2b\\x+4 & x+5 & x+2c\end{vmatrix}$ if $a,b,c$ are in A.P

asked Jan 21, 2015 by meena.p

1 answer

Solve for $x,$ $ (\sin ^{-1} \large\frac{1}{5}$$+\cos ^{-1} x)=1$

asked Jan 21, 2015 by meena.p

1 answer

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